A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... |
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Page 36
... therefore the two sides given make a quadrantal angle , or are perpendicular to each other . a Q. E. D. THEOREM V. Of all Rectilinear Figures in which all the Sides except one are known , the Greatest is that which may be Inscribed ...
... therefore the two sides given make a quadrantal angle , or are perpendicular to each other . a Q. E. D. THEOREM V. Of all Rectilinear Figures in which all the Sides except one are known , the Greatest is that which may be Inscribed ...
Page 54
... three equations , and obtaining , in expressions of known terms , the value of each of the unknown quantities , the others being exterminated by the usual processes . Each of these general methods has its peculiar advantages .
... three equations , and obtaining , in expressions of known terms , the value of each of the unknown quantities , the others being exterminated by the usual processes . Each of these general methods has its peculiar advantages .
Page 55
... when we speak of the sine , tangent , or secant , of an angle , we mean the sine , tangent , or secant , of the arc which measures that angle ; the radius of the circle employed being known . 4. It has been shown in the 2d vol .
... when we speak of the sine , tangent , or secant , of an angle , we mean the sine , tangent , or secant , of the arc which measures that angle ; the radius of the circle employed being known . 4. It has been shown in the 2d vol .
Page 57
... and are constituted of known terms , they may be represented by the same character ; suppose K : then shall we have 2K sin . A sin . B bc 2 2K bc sin . B ( iii . ) Hence we may immediately deduce a very important theorem for ...
... and are constituted of known terms , they may be represented by the same character ; suppose K : then shall we have 2K sin . A sin . B bc 2 2K bc sin . B ( iii . ) Hence we may immediately deduce a very important theorem for ...
Page 64
2A = it will be easy , when the sine of an arc is known , to find that of its half . For , substituting for cos A its value V ( R'- sin A ) , 2 sin AV ( R2 - sin ? A ) there will arise sin 2A = This squared gives R ' sin ?
2A = it will be easy , when the sine of an arc is known , to find that of its half . For , substituting for cos A its value V ( R'- sin A ) , 2 sin AV ( R2 - sin ? A ) there will arise sin 2A = This squared gives R ' sin ?
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A Course of Mathematics: In Three Volumes: Composed for the Use of the Royal ... Charles Hutton No preview available - 2016 |
A Course of Mathematics: In Three Volumes: Composed for the Use of the Royal ... Charles Hutton No preview available - 2016 |
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altitude angle assumed axis ball base beam becomes centre circle consequently construction Corol cosine curve denote determine diameter direction distance divided double draw drawn effect equal equation expression fall feet figure fluent fluxion force former given gives greater greatest half Hence inches known latter length less manner means measured meet motion moving nearly negative obtain opposite parallel perpendicular plane polygon position preceding PROBLEM produced proportional quantity radius ratio resistance respectively right line roots rule sides similar sine solid space sphere spherical square suppose surface tangent theor THEOREM theref third tion triangle velocity vertical weight whole
Popular passages
Page 65 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 116 - Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles (th.
Page 249 - Or, by art. 3 14 of the same, the pressure is equal to the weight of a column of the fluid, •whose base is equal to the surface pressed, and...
Page 82 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Page 335 - ... to secure uniformity, his trees were all felled in the same season of the year, were squared the day after, and the experiments tried the 3d day.
Page 166 - Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark.
Page 164 - ... preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz. that in general an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and that each root has the property of rendering, by its substitution in place of the unknown quantity, the aggregate of all the terms of the equation equul to nothing.
Page 74 - Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also, that the...
Page 261 - And when this is compared with the proportion of the velocity and length of gun in the last paragraph, it is evident that we gain extremely little in the range by a great increase in the length of the gun, with the same charge of powder. In fact the range is nearly as the 5th root of the length of the bore ; which is so small an increase, as to amount only to about a...
Page 74 - Prob. 12. How must three trees, A, B, C, be planted, so that the angle at A may be double the angle at B, the angle at B double the angle at C, and a line of 400 yards may just go round them ? Ans.
Bibliographic information
| Title | A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... Volume 3 of A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy, Charles Hutton |
| Author | Charles Hutton |
| Edition | 6 |
| Publisher | J. Johnson, 1811 |
| Original from | the New York Public Library |
| Digitized | 2 May 2006 |
| Export Citation | BiBTeX EndNote RefMan |